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The action of a Turingmachine is determined completely by (1) the current state of the machine (2) the symbol in the cell currently being scanned by the head and (3) a table of transition rules, which serve as the “program” for the machine.

The actions available to a Turingmachine are either to write a symbol on the tape in the current cell (which we will denote with the symbol in question), or to move the head one cell to the left or right, which we will denote by the symbols « and » respectively.

The complete state of a Turingmachine at any point during a computation may be described by the name of the state that the machine is in, the symbols on the tape, and the cell that is currently being scanned.

The concept of the Turingmachine is based on the idea of a person executing a well-defined procedure by changing the contents of an infinite number of ordered paper sheets that can contain one of a finite set of symbols.

While such machines may be physically impossible as they require unlimited storage and zero crashing probability, Turing completeness is often loosely attributed to physical machines or programming languages that would be universal if they had indefinitely enlargeable storage and were absolutely reliable.

Turing completeness is significant in that every plausible design for a computing device so far advanced (even quantum computers) can be emulated by a universalTuringmachine.

Thus, a machine that can act as a universalTuringmachine can, in principle, perform any calculation that any other computer is capable of (in other words, it is programmable).

A Turingmachine is an automaton which moves along a linear strip of data and performs certain actions according its state, which depends upon the data it has 'seen,' and the datum symbol that it is viewing.

Turing and Emil Post independently proved that determining the decidability of mathematical propositions is equivalent to asking what sorts of sequences of a finite number of symbols can be recognized by an abstract machine with a finite set of instructions.

The Turingmachine moves its tape head one symbol to the left or to the right, or does not move the tape head, depending on the value of the 'movement' attribute that is returned by the transition function.

If the Turingmachine moves the tape head to the right of the rightmost symbol, then a blank symbol is appended to the end of the tape and this new blank symbol becomes the current symbol.

If the Turingmachine moves the tape head to the left of the leftmost symbol, then a blank symbol is inserted at the beginning of the tape and this new blank symbol becomes the current symbol.

www.unidex.com /turing/utm.htm (914 words)

Turing machine(Site not responding. Last check: 2007-10-04)

Since a machine has only a finite number of internal states and of tape symbols, the state table of a machine is finite in length and can be stored on a tape.

Turingmachines may be thought of as conceptual devices for enumerating the elements of an infinite set (e.g., the theorems of a formal language), or as decision machines (e.g., deciding of any truth-functional formula whether it is a tautology).

Turing's definition of a machine was theoretical; it was not a practical specification for a machine.

The Turingmachine is an abstract machine introduced in 1936 by Alan TuringAlan Mathison Turing (June 23, 1912–June 7, 1954) was a British mathematician, logician, cryptographer, and war hero, and is widely considered to be the father of computer science.

The concept of a Turingmachine was used as an educational tool in the science fictionScience fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals.

Equivalently, it can be defined as a deterministic Turingmachine having an additional "write" instruction where the value of the write is uniformly distributed in the TuringMachine's alphabet (generally, an equal likelihood of writing a '1' or a '0' on to the tape.)...

The input is given in binary form on the machine's tape, and the output consists of the contents of the tape when the machine halts.

The problem with TuringMachines is that a different one must be constructed for every new computation to be performed, for every input output relation.

This is why we instroduce the notion of a universalturingmachine (UTM), which along with the input on the tape, takes in the description of a machine M. The UTM can go on then to simulate M on the rest of the contents of the input tape.

So, in effect your script simulates the finite state control of the UTM until the program is read to completion after which the UTM transforms into the turingmachine as described by the program.

The output of any turingmachine is the final state of the tape along with the informtion about the position on the tape where the turingmachine head comes to a halt.

Test your script with a turingmachine program that you will have to come up with for simulating the string search operation given binary data and the string to be searched known to the finite state control of the turingmachine as it will be defined (hard-coded) in your program.

www.cs.unm.edu /~luger/cs451/assignments/a7.html (335 words)

Turing Machine(Site not responding. Last check: 2007-10-04)

In 1937, Turing suggested a theoretical device, since called a TuringMachine, that became the basis of modern computing.

More precisely, a Turingmachine consists of: # A tape which is divided into cells, one next to the other.

The Turing test and intelligencedocument clarifing the meaning of the Turing test and suggests that meeting the Turing test is already in the process of being achieved

www.wikiverse.org /turing-machine (1858 words)

The Turing Machine and Universal Computation(Site not responding. Last check: 2007-10-04)

Turing put forward the question that if M is a TuringMachine and S a sequence of 0's and 1's, is there a TuringMachine that can decide if M ever halts when given S as input.

An oracle TuringMachine is described as a machine that is connected to an oracle.

Turing showed that the TuringMachine could simulate any other computingmachine and human beings are also like computers, (Before the publication of Turing’s1936 paper the term computer was generally applied to human begins), thus the Human computer could also be successfully simulated by the TuringMachine.

Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "universalTuringmachine", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.

www.nist.gov /dads/HTML/universalTur.html (132 words)

Alan Turing: a short biography - 3(Site not responding. Last check: 2007-10-04)

Turing worked in isolation from the powerful school of logical theory centred on Church at Princeton University, and his work emerged as that of a complete outsider.

The concept of 'the Turingmachine' is like that of 'the formula' or 'the equation'; there is an infinity of possible Turingmachines, each corresponding to a different 'definite method' or algorithm.

Additionally, the abstract UniversalTuringMachine naturally exploits what was later seen as the 'stored program' concept essential to the modern computer: it embodies the crucial twentieth-century insight that symbols representing instructions are no different in kind from symbols representing numbers.

Continue to the Scrapbook page on Alan Turing and his Turingmachines for more general information on the machine concept.

Machine 2 performs a divisibility test: the machine will stop with an X printed in the original blank square separating the numbers if and only if the number on the left divides exactly into the number on the right.

Machine 3 uses this divisibility test as the basis for a primality test: the machine stops with an X in the original square if and only if the number on the right is prime.

By convention a TuringMachine is understood to be a definition of a procedure, namely an "algorithm", for example, the detailed step by step procedure for controlling the automatic drive on my automobile.

Turing's negative solution was published in the Proceedings of the London Mathematical Society in 1936.

Turing reduced his procedure to simple steps that could be carried out, one step at a time, by a disciplined procedure.

This is a biographical illustration and portrait of a man named Alan Turing, drawn as and titled after the creation for which he is most famous.

Alan Turing was a shy and tragic man. One of the founders of modern computer science and the field of artificial intelligence, he dreamed of an abstract idea which came to be known as the TuringMachine — something we would recognize today as a computer, before such a thing ever existed.

Turing, he was openly homosexual at a time when such things were unacceptable.

The University of Pennsylvania and the Smithsonian made a great deal of it as the "birth of the Information Age".

The parallel between Turing and Zuse is explored by Thomas Goldstrasz and Henrik Pantle.

This writer fails to distinguish the UniversalTuringmachine from the general Turingmachine concept; he believes the Colossus was used by Turing on the Enigma and was 'essentially a bunch of servomotors and metal'...

A Universalmachine is a Turingmachine with the property of being able to read the description of any other Turingmachine, and to carry out what that other Turingmachine would have done.

Turing gave an exact description of such a Universalmachine in his paper (though with a few bugs).

Clearly, these "Universal"TuringMachines need legal controls, such as the INDUCE Act, in order that they not be abused for copyright infringement by those who would simulate copyrighted descriptions of other Turingmachines.

www.corante.com /importance/archives/005475.php (1060 words)

A Turing Machine in Conway's Game of Life, extendable to a Universal Turing Machine(Site not responding. Last check: 2007-10-04)

It is a very simple TuringMachine as it is limited to 3 states and 3 symbols.

The design for this TuringMachine is extendible by expanding the size of the Finite State Machine part and storing different numbers in the memory cells.

This is sufficient for a UniversalTuringMachine.

rendell.server.org.uk /gol/tm.htm (567 words)

What is the minimum number of states in a Universal Turing Machine? | Ask MetaFilter(Site not responding. Last check: 2007-10-04)

What is the absolute minimum number of states required in a TuringMachine (that uses binary tape) for it to be able to serve as a UniversalTuringMachine?

I'm looking into designing a visual aid to help explain the Turingmachine, and I want the system it depicts to be as simple as possible, yet sufficient (in theory at least) to operate as a UTM.

(The internet is loaded with UTM information, and references to "a minimum finite number of states" abound, but nothing seems to mention what that number actually happens to be, and I don't really have the time or the ability to reinvent the wheel)

formally de ned the s signi cant logical depth of an object x as the time required by a standard universalTuringmachine to generate x by a program that is no more than s bits longer than the shortest descriptions of x.

formally de ned the s signi cant logical depth of a string x as the time required by a standard universalTuringmachine to generate x by a program that is no more than s bits longer than the shortest descriptions of x.

However, Bennett [2, 3] has defined a complexity measure based on programs for universalTuringmachines that does capture the desired complexity criteria and is universal for all objects that can be digitally encoded.